Learning Neural Operators from Partial Observations via L...

Authors

Jingren Hou School of Computer Science and Technology, Beijing Jiaotong University, Beijing, China Beijing Key Laboratory of Traffic Data Mining and Embodied Intelligence, Beijing, China
Hong Wang University of Science and Technology of China
Pengyu Xu School of Computer Science and Technology, Beijing Jiaotong University, Beijing, China Beijing Key Laboratory of Traffic Data Mining and Embodied Intelligence, Beijing, China
Chang Gao School of Computer Science and Technology, Beijing Jiaotong University, Beijing, China Beijing Key Laboratory of Traffic Data Mining and Embodied Intelligence, Beijing, China
Huafeng Liu School of Computer Science and Technology, Beijing Jiaotong University, Beijing, China Beijing Key Laboratory of Traffic Data Mining and Embodied Intelligence, Beijing, China
Liping Jing School of Computer Science and Technology, Beijing Jiaotong University, Beijing, China Beijing Key Laboratory of Traffic Data Mining and Embodied Intelligence, Beijing, China

DOI:

https://doi.org/10.1609/aaai.v40i1.37001

Abstract

Real-world scientific applications frequently encounter incomplete observational data due to sensor limitations, geographic constraints, or measurement costs. Although neural operators significantly advanced PDE solving in terms of computational efficiency and accuracy, their underlying assumption of fully-observed spatial inputs severely restricts applicability in real-world application. We introduce the first systematic framework for learning neural operators from partial observation. We identify and formalize two fundamental obstacles: (i) the supervision gap in unobserved regions that prevents effective learning of physical correlations, and (ii) the dynamic spatial mismatch between incomplete inputs and complete solution fields. Specifically, our proposed LANO (Latent Autoregressive Neural Operator) introduces two novel components designed explicitly to address the core difficulties of partial observations: (i) a mask-to-predict training strategy that creates artificial supervision by strategically masking observed regions, and (ii) a Physics-Aware Latent Propagator that reconstructs solutions through boundary-first autoregressive generation in latent space. Additionally, we develop POBench-PDE, a dedicated and comprehensive benchmark designed specifically for evaluating neural operators under partial observation conditions across three PDE-governed tasks. LANO achieves state-of-the-art performance with relative error reductions ranging from eighteen to sixty-nine percent across all benchmarks under patch-wise missingness with missing rates below fifty percent, including real-world climate prediction. Our approach effectively addresses practical scenarios with missing rates of up to seventy-five percent, to some extent bridging the existing gap between idealized research settings and the complexities of real-world scientific computing.

How to Cite

Hou, J., Wang, H., Xu, P., Gao, C., Liu, H., & Jing, L. (2026). Learning Neural Operators from Partial Observations via Latent Autoregressive Modeling. Proceedings of the AAAI Conference on Artificial Intelligence, 40(1), 390–398. https://doi.org/10.1609/aaai.v40i1.37001

Issue

Section

AAAI Technical Track on Application Domains I